2022/09/01 by Takafumi Kouno, Kouno, Takafumi, Satoshi Naito +3 · 1 citation
Mathematics · #14M15 #20G42 #81R10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Primary 05E10 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary 14N15
paper · pdf · doi:10.48550/arxiv.2209.00255
openalex publication_date 2022/09/01 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
We provide identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules of extremal weight modules over a quantum affine algebra of type C. These identities express the product eμ gch Vx-(λ) of the (one-dimensional) character eμ, where μ is a (not necessarily dominant) minuscule weight, with the graded character gch Vx-(λ) of the level-zero Demazure submodule Vx-(λ) over the quantum affine algebra Uq(\mathfrakgaf) as an explicit finite linear combination of the graded characters of level-zero Demazure submodules. These identities immediately imply the corresponding inverse Chevalley formulas in the torus-equivariant K-group of the semi-infinite flag manifold QG associated to a connected, simply-connected and simple algebraic group G of type C. Also, we derive cancellation-free identities from the identities above of inverse Chevalley type in the case that μ is a standard basis element εk in the weight lattice P of G.